By "application" i'm guessing you mean what methods are best to train in?
I recommend training in tape in, because they are very easily fitted and the are quite popular, micro beads are a must because you'll get plenty of clients that are after a method that does minimal damage, this method is also quite popular. The micro weft is slowly getting much more popular as they also do minimal damage and give you a natural finish.
Keratin bonds are also good to train in although the hair is much more than the other methods and it definitely is more time consuming.
As for training I really can't recommend any schools to you as I live in Australia.
i say tapes, honestly i tell majority of my clients they are so fun to do and less fidgety. the other day i had a client who had a rihanna clipper cut on the side and i managed to fit the extensions on the hair, i wouldnt of been able to do that with i tips.
i say they look less fake, from a client perspective they are cheaper but i tell them that the best result is with tapes.